Physical theory and growing evidence suggests that under greenhouse gas driven global warming scenarios, extreme weather events will often become more intense. Heavy, regional precipitation events are among the principal weather extremes expected to evolve under warming. As the atmosphere warms, on average, atmospheric moisture holding capacity increases in many regions, which can increase the severity of precipitation extremes and consequences like flooding. At the regional and local scales relevant to stakeholders, uncertainty in extremes is large, but generally not well characterized, owing to long-standing gaps in scientific understanding of complex, small-scale physical processes that drive them.